Spin-flavour symmetry

For three light flavours and two spin states, an approximate $SU(6)$ spin-flavour symmetry acts on the six-dimensional single-quark spin-flavour space. A spatial ground-state three-quark colour singlet requires the symmetric representation of dimension $56$. Under flavour symmetry and ordinary spin rotations, it decomposes as $(10,4)\oplus (8,2)$: the baryon decuplet has spin $3/2$ and the baryon octet spin $1/2$. The product of spin and flavour factors can require a correlated sum, rather than a single unentangled product.